Russ-
My thoughts on your latest questions...
For what you are doing, a utility pot of at least 15 gallons would be good. They come in different dimensions (length vs. height combinations), but a standard one might be about 16-18" in diameter by about 16"+ high. Something this size will allow for the screening density you want, prevent having to re-pot frequently, and will be completely stable in the wind.
It sounds like the boxes in that Bamboo World link you provided have a bottom with drainage holes, but the bottom is supported off the ground. If I were using those, I would simply place the pots inside the box, and skip the bamboo barrier as unnecessary since the rhizomes would be contained in the pots and any that escaped through drainage holes could be easily pruned. And if you plant clumping bamboo you would not really have to worry about rhizomes escaping, anyway.
I would make a wooden X support to place under each pot so it is not sitting directly on the wood bottom as that will preserve the bottom longer, and you can make the X of a dimension that raises the top of the pot to whatever level you want in comparison to the planter. You're not likely to get much, if any, dirt falling out of the bottom of the container, and that can be hosed off the patio since you've got clearance. You will have some water on the patio, but that will be minimal once you learn how much to water them at a time (and I presume there is a slight slope to the patio to help drainage when it rains?).
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